A possible way to study the reionization of cosmic hydrogen is by observing the large ionized regions (bubbles) around bright individual sources, e.g. quasars, using the redshifted 21 cm signal. It has already been shown that matched filter-based methods are not only able to detect the weak 21 cm signal from these bubbles but also aid in constraining their properties. In this work, we extend the previous studies to develop a rigorous Bayesian framework to explore the possibility of constraining the parameters that characterize the bubbles. To check the accuracy with which we can recover the bubble parameters, we apply our method on mock observations appropriate for the upcoming SKA1-low. For a region of size greater than or similar to 50 cMpc around a typical quasar at redshift 7, we find that approximate to 20 h of integration with SICA1-low will be able to constrain the size and location of the bubbles, as well as the difference in the neutral hydrogen fraction inside and outside the bubble, with < less than or similar to 10 per cent precision. The recovery of the parameters are more precise and the signal-to-noise ratio of the detected signal is higher when the bubble sizes are larger and their shapes are close to spherical. Our method can be useful in identifying regions in the observed field that contain large ionized regions and hence are interesting for following up with deeper integration times.